# Rectified great stellated hecatonicosachoron

(Redirected from Ragishi)
Rectified great stellated hecatonicosachoron Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymRagishi
Coxeter diagramo5/2x3o5o (         )
Elements
Cells120 icosahedra, 120 great icosidodecahedra
Faces2400 triangles, 720 pentagrams
Edges3600
Vertices720
Vertex figureSemi-uniform Pentagonal prism, edge lengths 1 (base) and (5–1)/2 (side)
Measures (edge length 1)
Circumradius$\sqrt{\frac{5-\sqrt5}{2}} ≈ 1.17557$ Hypervolume$5\frac{205-63\sqrt5}{4} ≈ 80.15965$ Dichoral anglesGid–5/2–gid: 144°
Ike–3–gid: 120°
Central density20
Number of external pieces5160
Level of complexity20
Related polytopes
ArmyRox, edge length $\frac{3-\sqrt5}{2}$ RegimentRagishi
ConjugateRectified grand hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count43200
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The rectified great stellated hecatonicosachoron, or ragishi, is a nonconvex uniform polychoron that consists of 120 icosahedra and 120 great icosidodecahedra. Two icosahedra and five great icosidodecahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the great stellated hecatonicosachoron.

## Vertex coordinates

The vertices of a rectified great stellated hecatonicosachoron of edge length 1 are given by all permutations of:

• $\left(0,\,0,\,±1,\,±\frac{\sqrt5-1}{2}\right),$ • $\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$ along with even permutations of:

• $\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{5-\sqrt5}{4}\right),$ • $\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$ • $\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{4}\right),$ • $\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±1,\,±\frac{3-\sqrt5}{4}\right).$ ## Related polychora

The rectified great stellated hecatonicosachoron is the colonel of a regiment with 15 members. Of these, one other besides the colonel itself is Wythoffian (the rectified grand stellated hecatonicosachoron), two are hemi-Wythoffian (the small pentagrammal antiprismatoverted dishecatonicosachoron and pentagonal retroprismatoverted hexacosihecatonicosachoron), and one is noble (the great retropental hecatonicosachoron).

It has the same circumradius as the hexagonal-decagrammic duoprism.

Uniform polychoron compounds composed of rectified great stellated hecatonicosachora include: